The research undertaken during the period of this grant falls into two general categories (i) membrane biophysics and (ii) bacterial propulsion. This work will be performed in collaboration and/or correspondence with experimental laboratories engaged in studies on specific organisms. The models will be primarily directed towards understanding and explaining their experimental observations. However, previous experience assures that models directed at particular biological systems frequently lead to general principles that apply to a wider range of phenomena. The specific goals of this project are to model the following systems. 1. Membrane dynamics. We will address the formation of lipid droplets from the endoplasmic reticulum (ER) using models of lipid tilt. We consider this degree of freedom essential to explain vesicle fusion and scission that involve topological changes in membrane geometry. Using continuum models of lipid tilt, we will focus on the initiation and growth of the bud and its subsequent scission. Our model also allows us to model the flow of lipid in the membrane. This is important in dramatic membrane shape changes such as that in the cubic-to-lamellar transition in intracellular organelles. This work will be carried out in collaboration with Prof. D. Steigmann (UC Berkeley). 2. Bacterial propulsion. We will address novel propulsive mechanisms that have not been previously modeled, and for which experimental observations provide clues to their modus operandi. Our attention will be directed at (i) the gliding A-motility system of Myxococcus xanthus and related bacteria (e.g. Flavobacteria), and (ii) the swimming of the cyanobacterium, Synechococcus. This work will be carried out in collaboration with the experimental laboratories of Professor D. Zusman (UC Berkeley) and Dr. B. Brahamsha (Scripps). The mathematical modeling will be carried out in collaboration with Professor J. Neu (UC Berkeley). PUBLIC HEALTH RELEVANCE: Each of these projects investigates mathematical models whose structure and properties have not been fully explored heretofore. The membrane model explores the lipid tilt degree of freedom that has been largely ignored, but which we are convinced is critical in driving topological changes in biomembrane structure. The mechanism that we propose for gliding bacteria is entirely new, the mathematical structures are novel as are some of the numerical and perturbation methods to be developed to analyze them.